Nodule boundary detection

ABSTRACT

A method of detecting the extent of a lung nodule in a scan image comprises fine segmenting ( 14 ) a region around the nodule into foreground and background, filling holes within foreground areas ( 16 ), region growing the foreground ( 18 ) to identify an initial region of interest, determining a mask ( 20 ) by enlarging the initial region to contain background and to exclude other foreground regions, determining a spatial map ( 26 ) of connectivity within the mask to a point within the initial region, region growing ( 28 ) within the mask and determining the maximum edge contrast ( 30 ) during region growing. The region of maximum edge contrast identifies the extent of the nodule ( 32 ). The position of the nodule may a seed point identified by the user ( 12 ). Most preferably, an optimum seed point is determined by iterative determination of seed points ( 22, 24 ) so that the determined extent of the nodule is substantially independent of the precise location of the seed point identified by the user.

RELATED APPLICATIONS

This application claims the benefit of the filing date of GB PatentApplication No. 0411064.9, filed May 18, 2004, which is incorporatedherein by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates to a method of detecting the boundary of anodule in an image previously scanned from a human or animal body,particularly but not exclusively in a computed tomography (CT) image ofthe lung, and more particularly but not exclusively to detecting theboundary of a lung nodule in a low-contrast area, such as attached to ablood vessel or in an isolated position within the lung. The method maybe implemented using a computer, and the invention encompasses softwareand apparatus for carrying out the method.

BACKGROUND OF THE INVENTION

The mortality rate for lung cancer is higher than that for other kindsof cancers around the world. Detection of suspicious lesions in theearly stages of cancer can be considered the most effective way toimprove survival. Lung nodule detection is one of the more challengingtasks in medical imaging. Lung nodules may be difficult to detect on CTscans because of low contrast, small size, or location of the nodulewithin an area of complicated anatomy. In particular, it is difficult todetect the extent of a lung nodule purely by inspection, when the noduleis attached to a blood vessel or vessels or surrounded by structure witha similar intensity to the nodule. Detection of the size or extent of alung nodule is important for accurate diagnosis.

One problem with known techniques is a tendency to include part of ablood vessel with the detected nodule, because of an inability todistinguish between the two.

Another problem with known techniques is that they are over-reliant onthe setting of detection parameters by the operator, and there are noideal parameter values which are applicable to all scan images.

Another problem with known techniques is that they impose a model whichis not applicable for all types of lung nodule.

U.S. Pat. No. 4,907,156 discloses a method of detecting lung nodules bypixel thresholding, followed by circularity and/or size testing ofcontiguous pixels above the threshold.

WO-A-9942950 discloses a method of lung nodule detection involvingpre-processing the image to identify candidate nodules, performing imageenhancement on a candidate nodule, and identifying whether the candidatenodule is a false positive by obtaining a histogram of accumulated edgegradients as a function of radial angle.

WO-A-02085211 discloses a method of automatic lung nodule detectionusing adaptive threshold segmentation.

U.S. Pat. No. 6,654,728 discloses a method of discriminating nodules ina chest scan images using fuzzy logic classification.

WO-A-0346831 discloses a computerized lung nodule detection method whichcreates a mask image by linear interpolation between first and last CTsection images, warped to match intermediate CT section images.

The article ‘Automated Lung Nodule Detection at Low-Dose CT: PreliminaryExperience’ by Goo JM et. al., Korean J Radiol 4(4), December 2003discloses a technique for detecting lung nodules using grey-levelthresholding and 3D region growing, together with 3D shape analysis todistinguish nodules from blood vessels.

SUMMARY OF THE INVENTION

According to an embodiment of the present invention, there is provided amethod of detecting the boundary or extent of a lung nodule in a scanimage, comprising: identifying the location of the nodule by obtaining aseed point within the nodule; fine segmenting the region of interestinto foreground and background; region growing a nodule foreground areafrom the seed point; determining a mask by enlarging the noduleforeground to contain background surrounding the nodule foreground areaand to exclude other foreground not connected to the nodule foreground;determining a connectivity map of the strength of connectivity of eachpoint within the mask to the seed point, and applying a connectivitycriterion to detect the boundary or extent of the lung nodule.

Preferably, the fine segmentation is based on local contrast. Oneadvantage of using local contrast is that a boundary can be detectedbetween adjacent objects of similar intensity, such as a nodule and ablood vessel. In this case, the fine segmentation can establish aboundary of background between the foreground objects. Another advantageis that a low intensity object can be identified as foreground even if ahigh intensity object is also present in the scan image, but is notclose enough to the low intensity object to raise the local segmentationthreshold above the low intensity value and therefore cause the lowintensity object to be identified as background.

Fine segmentation based on local contrast can lead to spurious detectionof foreground objects in background areas of low, but variableintensity. Such variations in background intensity are often due toscanning artefacts such as shadows, or objects that are not likely to benodules. Hence, detection of these spurious foreground objects isadvantageous, because they are then excluded from the mask and do notaffect subsequent processing steps.

Preferably, background ‘holes’ surrounded by foreground after the finesegmentation are converted to foreground. These background holes aretypically a result of the fine segmentation within objects of high, butvariable intensity and do not represent real low-intensity holes.

Preferably, the connectivity criterion is adaptively determined byregion growing from the seed point in the connectivity map, withoutextending beyond the mask, and determining the maximum boundary contrastduring region growing. The extent of the nodule is determined as theregion boundary of maximum boundary contrast during region growing. Thisboundary represents the point at which the region is most disconnectedfrom the background, and is therefore most likely to represent theboundary of the nodule. This technique is adaptive to the contrast ofthe nodule to its background, and does not require arbitrarythresholding of the connectivity map.

The region growing may be weighted according to the strength ofconnectivity in the connectivity map of each point neighboring thecurrent region, so that neighboring points having higher connectivityare added to the region before neighboring points having lowerconnectivity. This improves the likelihood that the boundary at somestage during region growing corresponds to the actual boundary of thenodule.

The region growing may be weighted inversely to the distance of eachpoint neighboring the current region from the centre of the currentregion, so that points closer to the centre are added to the regionbefore points further from the centre. This gives the region a tendencyto sphericity, which is common to actual nodules, without imposing arigid shape to the region.

Preferably, an optimum seed point is determined iteratively so that themask, and therefore the detected boundary of the nodule is substantiallyindependent of the precise location of an initial seed point, whichserves only to identify the nodule of interest.

The detected extent or boundary can be displayed graphically, and/or anyderived metric such as the size, shape, volume, mass or density of thenodule may be output.

The method can be applied to a single scan slice, but is preferablyapplied to a three-dimensional (3D) image constructed from a pluralityof sequential slices.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing a CT scanner and a remote computerfor processing image data from the scanner.

FIG. 1 a is an example computer system according to an embodiment of thepresent invention.

FIG. 2 is a flowchart of an algorithm according to an embodiment of thepresent invention.

FIG. 3 shows a series of slices of a CT scan image.

FIG. 4 shows the slices of FIG. 1 after a fine segmentation step.

FIG. 5 shows the slices of FIG. 4 after a hole-filling step.

FIG. 6 shows an initial region identified in the slices of FIG. 3.

FIG. 7 shows an enlarged initial region used as a mask area.

FIG. 8 shows a fuzzy map within the mask area.

FIG. 9 shows the determined extent of a nodule superimposed on theinitial image.

FIG. 10 is a diagram illustrating the determination of fuzzyconnectivity according to an embodiment of the present invention.

FIGS. 11 and 12 show the results of detection based on fuzzyconnectivity region growing using predetermined fixed region statistics.

FIGS. 13 and 14 show the results when the region statistics areestimated by the algorithm from the scan image.

FIG. 15 a to 15 d illustrate the reproducibility of the algorithm whendifferent seed points are selected within the nodule.

FIG. 16 a to 16 d show two different scan images together with theirfuzzy maps.

FIG. 17 shows the intensity values of an object within an imageaccording to an embodiment of the present invention.

FIG. 18 is a schematic graph of peripheral contrast during regiongrowing in the fuzzy map according to an embodiment of the presentinvention.

FIG. 19 shows a binary circle and blurred circles used to test regiongrowing.

FIGS. 20 and 21 show a synthetic image and the result of peripheralcontrast region growing on it.

FIGS. 22 a to 22 c show the results of region growing with a real imageas input (both 2D and 3D).

FIGS. 23 a to 23 c show a real image, a fuzzy map based on the images,and the results of region growing on the fuzzy map.

FIGS. 24 a to 24 c show comparative results using different techniqueson a nodule attached to a blood vessel.

FIGS. 25 a to 25 c show comparative results on a low-contrast nodule.

FIGS. 26 a to 26 c show comparative results on an isolated nodule.

FIG. 27 a to 27 c show comparative results on a near-wall nodule.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

CT Image

Each embodiment is performed on series of CT image slices obtained froma CT scan of the chest area of a human or animal patient. Each slice isa 2-dimensional digital grey-scale image of the x-ray absorption of thescanned area. The properties of the slice depend on the CT scanner used;for example, a high-resolution multi-slice CT scanner may produce imageswith a resolution of 0.5-0.6 mm/pixel in the x and y directions (i.e. inthe plane of the slice). Each pixel may have 32-bit grayscaleresolution. The intensity value of each pixel is normally expressed inHounsfield units (HU). Sequential slices may be separated by a constantdistance along the z direction (i.e. the scan separation axis); forexample, by a distance of between 0.75-2.5 mm. Hence, the scan image isa three-dimensional (3D) grey scale image, with an overall sizedepending on the area and number of slices scanned.

The present invention is not restricted to any specific scanningtechnique, and is applicable to electron beam computed tomography(EBCT), multi-detector or spiral scans or any technique which producesas output a 2D or 3D image representing X-ray absorption.

As shown in FIG. 1, the scan image is created by a computer 4 whichreceives scan data from a scanner 2 and constructs the scan image. Thescan image is saved as an electronic file or a series of files which arestored on a storage medium 6, such as a fixed or removable disc. Thescan image may be processed by the computer 4 to identify the extent ofa lung nodule, or the scan image may be transferred to another computer8 which runs software for processing the image as described below. Theimage processing software may be stored on a carrier, such as aremovable disc, or downloaded over a network.

FIG. 1 a illustrates an example computer system 200, in which thepresent invention can be implemented as programmable code. Variousembodiments of the invention are described in terms of this examplecomputer system 200. After reading this description, it will becomeapparent to a person skilled in the art how to implement the inventionusing other computer systems and/or computer architectures.

The computer system 200 includes one or more processors, such asprocessor 204. Processor 204 can be a special purpose or a generalpurpose digital signal processor. The processor 204 is connected to acommunication infrastructure 206 (for example, a bus or network).Various software implementations are described in terms of thisexemplary computer system. After reading this description, it willbecome apparent to a person skilled in the art how to implement theinvention using other computer systems and/or computer architectures.

Computer system 200 also includes a main memory 208, preferably randomaccess memory (RAM), and may also include a secondary memory 210. Thesecondary memory 210 may include, for example, a hard disk drive 212and/or a removable storage drive 214, representing a floppy disk drive,a magnetic tape drive, an optical disk drive, etc. The removable storagedrive 214 reads from and/or writes to a removable storage unit 218 in awell known manner. Removable storage unit 218, represents a floppy disk,magnetic tape, optical disk, etc. which is read by and written to byremovable storage drive 214. As will be appreciated, the removablestorage unit 218 includes a computer usable storage medium having storedtherein computer software and/or data.

In alternative implementations, secondary memory 210 may include othersimilar means for allowing computer programs or other instructions to beloaded into computer system 200. Such means may include, for example, aremovable storage unit 222 and an interface 220. Examples of such meansmay include a program cartridge and cartridge interface (such as thatfound in video game devices), a removable memory chip (such as an EPROM,or PROM) and associated socket, and other removable storage units 222and interfaces 220 which allow software and data to be transferred fromthe removable storage unit 222 to computer system 200.

Computer system 200 may also include a communication interface 224.Communication interface 224 allows software and data to be transferredbetween computer system 200 and external devices. Examples ofcommunication interface 224 may include a modem, a network interface(such as an Ethernet card), a communication port, a Personal ComputerMemory Card International Association (PCMCIA) slot and card, etc.Software and data transferred via communication interface 224 are in theform of signals 228 which may be electronic, electromagnetic, optical,or other signals capable of being received by communication interface224. These signals 228 are provided to communication interface 224 via acommunication path 226. Communication path 226 carries signals 228 andmay be implemented using wire or cable, fiber optics, a phone line, acellular phone link, a radio frequency link, or any other suitablecommunication channel. For instance, the communication path 226 may beimplemented using a combination of channels.

In this document, the terms “computer program medium” and “computerusable medium” are used generally to refer to media such as removablestorage drive 214, a hard disk installed in hard disk drive 212, andsignals 228. These computer program products are means for providingsoftware to computer system 200.

Computer programs (also called computer control logic) are stored inmain memory 208 and/or secondary memory 210. Computer programs may alsobe received via communication interface 224. Such computer programs,when executed, enable the computer system 200 to implement the presentinvention as discussed herein. Accordingly, such computer programsrepresent controllers of the computer system 200. Where the invention isimplemented using software, the software may be stored in a computerprogram product and loaded into computer system 200 using removablestorage drive 214, hard disk drive 212, or communication interface 224,to provide some examples.

Detection of Pulmonary or Isolated Nodules

An embodiment comprises image-processing software for detecting theextent of pulmonary nodules, which appear attached to one or more bloodvessels within a CT image, or isolated nodules, which are not adjacentto any other feature in the CT image. This embodiment uses afuzzy/contrast region-growing scheme as described below. A flowchart ofthe algorithm is shown in FIG. 2, and references to step numbers in thedescription below are to steps in this flowchart.

A sample scan image is shown in FIG. 3, and the results of progressiveprocessing steps on the image are shown in FIGS. 4 to 8. An output ofthe algorithm, based on the sample scan image, is shown in FIG. 9.

1. Fuzzy/Contrast Region Growing

The user of the software inspects the image to identify an areacontaining a nodule and selects a seed point (step 12), within aspecified one of the slices, which appears to be within the nodule. Theremainder of the image processing is preferably carried out without userinput; hence, the process is semi-automated.

In an alternative embodiment, the user may be required to identify anarea containing a nodule, for example by drawing a box or other shapearound the area. The seed point may be derived from that area, forexample by taking as the seed point the centre of the area or the pointhaving the highest intensity within the area.

The user of the software may be a radiologist, who can be relied upon toidentify a point within a nodule. The user may instead identify a pointclose to a nodule, but not falling within it. As will be explained inmore detail below, the method derives an optimum seed point which isinsensitive to the precise seed point location chosen by the user, evenin some cases where the initial seed point is outside but close to anodule. However, if the initial seed point is clearly in a backgroundarea, because the intensity at the seed point is low, the initial seedpoint may be moved automatically to a nearby point of high intensitybefore the rest of the algorithm is applied.

In an alternative embodiment, the seed point may be identified from thescan image automatically, and input to the processing steps below. Inthat case, no user input is required, so that the process becomes fullyautomatic.

1.1 Find Foreground Region

First, a rough estimate is obtained of the extent of the region by meansof a local threshold-based segmentation process (step 14). A local 3Dvolume of about 3 cm in each direction (for example, 61×61×21 pixels at0.5 mm/pixel in the x and y directions, 1.5 mm separation in the zdirection), centered on the seed point, is cropped from the whole 3Dimage, and a local adaptive segmentation algorithm is performed using alocal 3D mask of 11×11×3 pixels, so as to segment the image into aplurality of connected objects, as described below. Alternatively, a 2Dlocal mask of 11×11 cm may be used.

Fine Segmentation

The local mask is used to derive a threshold intensity value for eachpoint. This means that the threshold is sensitive to the local contrastand can distinguish low contrast nodules from their background.

The threshold intensity is set to be the mean of the centroids of theintensity above and below the threshold.

The specific algorithm proceeds as follows:

-   -   1) For each pixel within the local volume:        -   a. Define the local mask for that pixel        -   b. Set initial threshold intensity as the average intensity            within the mask        -   c. Calculate a histogram of intensity within the mask area        -   d. Repeat:            -   i. Calculate the centroid C1 of the part of the                histogram below the threshold intensity            -   ii. Calculate the centroid C2 of the part of the                histogram above the threshold intensity            -   iii. Update the threshold to the mean of C1 and C2        -   e. Until the threshold converges to the mean of C1 and C2        -   f. Shift the threshold by a constant intensity value, which            is predetermined according to the application        -   g. If the intensity of the current pixel is higher than the            shifted threshold, define this pixel as foreground;            otherwise, define it as background    -   2) Next pixel within the local volume        The result of fine segmentation on the sample image is shown in        FIG. 4. Note that FIGS. 4 to 7 are binary images; any grey        levels in the images are printing artefacts.

Fill Holes

The foreground objects acquired by fine segmentation may include ‘holes’i.e. background pixels surrounded by foreground pixels. This arisesbecause of the sensitivity of the fine segmentation to small localdifferences in contrast. Since the foreground objects may representnodules, they are expected to be solid. Hence, a hole-filling algorithmis used to fill such holes (step 16), in other words to convert them toforeground pixels. Any suitable hole-filling algorithm may be used. Forexample, a polygon is fitted to an object containing a hole within aslice, and the pixels within the polygon are all set as foreground.

The result of hole filling in the sample image is shown in FIG. 5.

Recover Object Containing Seed

The slice which contains the seed point will normally comprise manysegmented regions. The region which contains the seed point isdetermined using a 3D binary region-growing scheme (step 18).

Binary Region Growing in Initial Slice

The binary region-growing algorithm is first performed on the slicecontaining the seed point, as follows:

-   -   1) Label the seed point 3D pixel (‘voxel’) as belonging to the        desired region    -   2) Assign the same label to all neighboring foreground voxels    -   3) Repeat        -   a. Take each labeled voxel and assign the same label to each            of its neighboring foreground voxels    -   4) Until there are no more neighboring foreground voxels.

In other words, the label propagates to neighboring foreground voxels,starting with the seed point. Neighboring voxels are those within theslice that are displaced by one pixel spacing in the horizontal (x)and/or vertical (y) direction.

One possible implementation of the binary region-growing algorithminvolves the use of a stack to store unlabelled neighboring voxels. Asis well known, a stack is last-in, first-out data structure in which thelast element added or ‘pushed’ onto the stack is the first element whichcan be retrieved from or ‘popped’ off the stack. The implementationproceeds as follows:

-   -   1) Push seed point onto stack    -   2) Repeat        -   a. Pop voxel off stack        -   b. Assign label to popped voxel        -   c. Push all adjacent unlabelled foreground voxels onto stack    -   3) Until stack is empty

Connected Regions

Connected regions in adjacent slices, or in the z direction generally,are determined using the binary region-growing algorithm describedabove, but taking as the seed point the pixel having the same x and ycoordinates as the seed point in the initial slice. In other words, theseed point is displaced in the slice spacing direction (z) to generate aseed point in the current slice and the corresponding regions inadjacent slices are labeled in the same way.

The user may choose a seed point close to the edge of a nodule in aslice, which no longer falls within the nodule if directly transposedinto the next slice. To solve this problem, in one alternative the seedpoint in the new slice may have the x and y coordinates of the centre ofthe labeled region in the previous slice. In a second alternative, oncethe labeled region has been determined in one slice, a circular core ofpixels is defined around the centre of the labeled region. A foregroundpixel in the new slice having the x and y coordinates of one of the corepixels in the old slice may be taken as the seed pixel in the new slice.

If the seed point in the new slice is not a foreground pixel, or thereare no foreground pixels in the displaced core of the secondalternative, then no more slices are considered in that direction. Oncethe regions have been connected in both directions from the initialslice, the process of identifying connected regions ends, with a singlelabeled 3D region encompassing the seed point. The labeled region in thesample image is shown in FIG. 6.

Foreground Region

The 3D labeled region encompassing the seed point is defined as theforeground region F; this region is expanded as described below, toserve as a mask for further processing.

1.2 Calculate Mask by Augmenting Initial Region

The foreground region F is expanded using a distance transform method toobtain a mask M containing both foreground and background (step 20).This is important, since lack of background will result in non-optimalestimation of parameters used in subsequent region-growing algorithms.The proportions of foreground and background may be approximately equal.

A known 2D distance transform method is applied to the inside part ofthe foreground region F in each slice, and the maximum distance S to theboundary is obtained, indicating the size of the foreground region. The2D distance transform method is then applied to the outer side of theregion, until the boundary of the expanded region has a distance S fromthe boundary of the foreground region F.

Next, the foreground objects segmented by the fine segmentation processthat are not labeled as part of the foreground region F are removed fromexpanded region. The expanded region including the foreground region F,but with the unlabelled foreground objects removed, is defined as a maskM. A background region B is defined by subtracting the foreground regionF from the mask M. The mask M, the foreground region F and thebackground region B are used for subsequent calculations. The mask M forthe sample image is shown in FIG. 7.

2. User-independent Seed Point

As described so far, the definition of the mask M depends on theselection of the seed point by the user. For the results of thedetection algorithm to be reproducible, a user-independent seed pointmust be obtained. This is done by defining an ‘optimum union mask’ M₀,which is initially a null region.

At the beginning of each iteration, M₀ is replaced by the union of M andM₀. A central core or ‘yolk’ of the mask M₀ is found using a distancetransform method to erode k layers of the mask M₀. The pixel withhighest intensity within the yolk of the mask M₀ (or optionally, thehighest intensity point on the longest line in the z direction withinthe yolk) is defined as the seed point S₀ (step 22) and the entireprocess described above from ‘1.1

Find Foreground Region’ (steps 14 to 22) is repeated with S₀ instead ofthe initial user-selected seed point. The process is repeated until M₀converges to M, to within a predetermined degree (step 24).

The process can be summarized in pseudo-code as follows:M₀=0Do

{ FindUnion(M₀,M ) FindYolk(M₀,Yolk) S₀ = GetMaxIntensityPoint(Yolk) M =Find Mask(M₀, S₀) } while(M₀! = M )

The optimum seed point S₀ is taken as the highest intensity point on thelongest line in the z direction within the mask. If it is not the sameas the user-provided seed point, the optimum seed point is taken as thenew seed point.

All subsequent steps are performed using the optimum mask M₀ and optimumseed point S₀. Foreground segmented objects excluded by the finesegmentation and binary growing, and therefore falling out side the maskM₀, cannot therefore affect the determined extent of the nodule.

3. Calculate Statistics

The mean and the standard deviation of the intensity and gradientdistributions of the foreground and background regions F and B aredetermined. The mean of the background intensity μ_(B), the mean of theforeground intensity μ_(F), the standard deviation of the backgroundintensity σ_(B) and the standard deviation of the foreground intensityσ_(F) are calculated. A parameter ε is estimated by counting the numberof the foreground standard deviations σ_(F) that the seed point is awayfrom the background mean intensity μ_(B) and this is taken as themeasure of the contrast, which is subsequently used in constructing afuzzy map as described below.

4. Construct Fuzzy Connected Map

A fuzzy object extraction technique is used to define a 3D map of fuzzyconnectivity of each pixel within the mask M₀ with respect to theoptimum seed point S₀ (step 26). A fuzzy affinity function betweenadjacent pixels is defined and the fuzzy connectivity between each pixeland the optimum seed point S₀ is derived by finding the affinity along apath between the pixel and the optimum seed point S₀.

The fuzzy connectivity between two points (not necessarily adjacent) isobtained by considering the path with the strongest affinity between twopoints. The path with the strongest affinity is chosen as the best pathand the strength of each path is equal to that of the weakest affinityof adjacent points along the path. This concept is illustrated in FIG.10, where two possible paths between points P1 and P10 are depicted.Think of this as a set of ropes tied together with different thicknessesand therefore different strengths. If the top chain of ropes (from P1 toP10) is pulled apart, it will break at the P2-P3 link; while the bottomset of ropes will break at the link P8-P9. Therefore the bottom rope isstronger than the top one with the strength equal to the strength ofP8-P9 link. The strength between two adjacent points is the affinitybetween those points.

The affinity between two spatial elements (spels)—either 2D pixels or 3Dvoxels—is a measure of the probability that they belong to the sameobject. This probability is a function of closeness (i.e. Euclidiandistance) and the similarity of the image features (i.e. intensity)between those spels. Fuzzy affinity must satisfy the followingconditions:Reflectivity: for all (x,x)εX×X, μ(x,x)=1 andSymmetric: for all (x,y)εX×X, μ(x,y)=μ(y,x)where μ (μ:X×X−>[0,1]) represents the fuzzy affinity for a 2-aryrelation. The first condition indicates that the fuzzy affinity of aspel to itself is always 1, and the second condition indicates that thefuzzy affinity of point 1 to point 2 is the same as that of point 2 topoint 1.

The general model for fuzzy affinity is given by:μ_(k)=(c,d)=h(μ_(a)(c,d),f(c),f(d),c, d)where h is a scalar value with range [0,1], c and d are image locationsof two spels, and f(i) is the intensity of spel i. μa is an adjacencyfunction based on distance between two spels which, for n-dimensionalcoordinate spels, is given by,

${\mu_{a}\left( {c,d} \right)} = \left\{ \begin{matrix}{1,} & {{{if}\mspace{14mu}\sqrt{\sum\limits_{i = 1}^{n}\left( {c_{i} - d_{i}} \right)^{2}}} \leq 1} \\{0,} & {otherwise}\end{matrix} \right.$

A simplified shift invariant version is defined asμ_(k)(c,d)=μ_(a)(c,d)└ω_(i) h _(i)(f(c),f(d))+ω_(g)(1.0−h_(gk)(f(c),f(d)))┘if c≠d, andμ_(k)(c,c)=1where the subscripts ‘i’ represents the calculations related tointensity and ‘gk’ represents the calculations related to gradientvalues in relevant direction (which could be x, y, z) respectively.ω_(i) and ω_(g) are free parameter weight values whose sum is 1. Thevalue of 0.9 for ω_(i) and 0.1 for ω_(g) has been chosen to allowintensity similarity to have more effect. The fuzzy affinity that wasused for the current function is:

${h_{i}\left( {{f(c)},{f(d)}} \right)} = {\mathbb{e}}^{- \frac{{\lbrack{{{({1/2})}{({{f{(c)}} + {f{(d)}}})}} - m_{i}}\rbrack}^{2}}{{(S_{d})}^{2}}}$${h_{gx}\left( {{f(c)},{f(d)}} \right)} = {\mathbb{e}}^{- \frac{{\lbrack{{({{{{f{(c)}} - {f{(\mathbb{d})}}}}/{\mathbb{d}x}})} - m_{gx}}\rbrack}^{2}}{{(S_{gx})}^{2}}}$${h_{gy}\left( {{f(c)},{f(d)}} \right)} = {\mathbb{e}}^{- \frac{{\lbrack{{({{{{f{(c)}} - {f{(\mathbb{d})}}}}/{\mathbb{d}y}})} - m_{gy}}\rbrack}^{2}}{{(S_{gy})}^{2}}}$${h_{gz}\left( {{f(c)},{f(d)}} \right)} = {\mathbb{e}}^{- \frac{{\lbrack{{({{{{f{(c)}} - {f{(\mathbb{d})}}}}/{\mathbb{d}z}})} - m_{gz}}\rbrack}^{2}}{{(S_{gz})}^{2}}}$where m_(i), s_(i), m_(g) and s_(g) are the Gaussian parameters for theintensity and gradient. These can be predefined, or are estimated from asmall region around the seed point as described below.

Parameter Calculation

The mean and standard deviation σ of the intensity and gradient arecalculated over all points within the optimum mask M₀. The parametersrelated to the gradients are computed in three directions (x, y and z)separately. The corresponding σ are calculated based on the differencebetween maximum and minimum gradient.

The calculation of the statistics is now described in more detail. Theparameter m_(i) is taken as the intensity of the seed whereas m_(gx),m_(gy) and m_(gz) are taken as the means of the gradients in x-, y-, andz-direction respectively. The parameters S_(gx), S_(gy) and S_(gz) arethe standard deviation of the gradients in their respective direction.

The standard deviation (S_(d)) appearing in the affinity expressionplays a major role in the formation of the fuzzy map and hence thedetermination of the boundary of the nodule. If it is too big, theaffinity curve will be relatively flat. Resultantly, the backgroundregion will have higher affinity and region growing will result inover-segmentation. On the other hand, if it is too small, the shape ofthe affinity curve will be narrow and the foreground will have lessaffinity with the seed and the result would be under-segmented. Ideally,the curve should be spread to such an extent that the background hasminimal but finite affinity with the seed.

Isolated nodules are under-segmented and pulmonary nodules areover-segmented if no correction is made for the standard deviation ofthe affinity curve. Also, it has been observed that isolated noduleshave higher contrast than pulmonary nodules. We therefore adjust S_(d)by taking into consideration the above findings. A factor f_(t) isdetermined and multiplied by the S_(F) (foreground standard deviation)to get a value of S_(d) which is actually used in the fuzzy expression.

t-Value as a Measure of Contrast

The significance of the difference of means of two samples can bemeasured by a statistic called Students t. We use this as an indicatorof the contrast between the foreground region F and the backgroundregion B. Let N_(F) be the number of the voxels in the foreground regionF and N_(B) be the number of voxels in the background region B. Letx_(i) be the intensity at voxel i. μ_(F) and μ_(B) are the means of theforeground and background regions.

For two distributions having same variance, the t-value is calculated asfollows:

First, the standard error of the difference of the means from the pooledvariance is calculated as:

${Se} = \sqrt{\left\lbrack {\frac{{\sum\limits_{i \in A}\left( {x_{i} - \mu_{F}} \right)^{2}} + {\sum\limits_{i \in B}\left( {x_{i} - \mu_{B}} \right)^{2}}}{N_{F} + N_{B} - 2}\left( {\frac{1}{N_{F}} + \frac{1}{N_{B}}} \right)} \right\rbrack}$

The t-value is computed as:

$t = \frac{\mu_{F} - \mu_{B}}{Se}$

A higher value of t represents higher contrast. It has been observedthat for isolated nodules the t-value is lower than for those attachedto blood vessel, indicating that the isolated nodules have high partialvolume effect.

We use this information to expand/limit the affinity Gaussian curve bymodifying the standard deviation. For lower t-values, the curve isnarrow and does not reach to the background mean, so the curve isexpanded until the background has some affinity. For higher t-values,the background will have higher affinity, as it is closer to foreground,so the fuzzy affinity curve is made narrow by reducing its standarddeviation. The inventor has conducted experiments and found an empiricalrelationship as follows.

A factor f is defined as:

$f = \frac{\left( {t - 30} \right)}{30}$

The values are clipped to 1(−1) if f-value is greater (lower) than1(−1).

-   -   If f>0, f is multiplied by 2.5.    -   If f<0, it is multiplied by 3.

Let S_(F) and S_(B) be the standard deviations of the foreground andbackground regions respectively.

S_(F) is divided by 1.25 to make it more aggressive to ensure that weget more regions for isolated nodules.f _(t)=(x _(seed)−(μ_(B) +S _(B) *f))/S _(F)

-   -   f_(t) is limited between 1.5 to 9.

Finally, the standard deviation is updated as:S _(d) =f _(t) ×S _(F)

Fuzzy Map Algorithm

The parameters of the fuzzy map algorithm are as follows:

-   -   a) an n-dimensional (nD) array to hold the fuzzy connectivity of        the voxels.    -   b) a queue (Q) to which potential spels are added.    -   c) a threshold value (x).    -   d) f_(o)(c) is the fuzzy connectivity of spel c    -   e) μ_(k)(c, d) is the fuzzy affinity between two adjacent spels        ‘c’ and ‘d’.

The algorithm proceeds as follows:

Begin:

-   -   1. set all nD cells to zero except for the seed value.    -   2. push all spels whose fuzzy affinity to the seed is more than        zero, i.e. μ_(k)(o, c)>0 to Q.    -   while Q not empty    -   3. remove a spel c from Q    -   4. if (f_(o)(c)<x) then    -   5. find f_(max)=max[min(f_(o)(d), μ_(k)(c, d))]    -   6. if f_(max)>f_(o)(c) and f_(max)>x then    -   7. set f_(o)(c)=f_(max)    -   8. push all spels e such that μ_(k)(o, e)>0 to Q.    -   endif    -   endif    -   endwhile

Explanation:

-   Step 1: The seed is the only spel in the object.-   Step 2: The immediate neighboring spels with fuzzy affinity more    than zero are considered.-   Step 3: If its connectivity is higher than threshold, no need to    check it again.-   Step 4: The neighbors added in step 2 are examined one by one-   Step 5: Find which among all neighboring spels has the strongest    link. The strength of each link is the minimum of the fuzzy    connectivity value of the neighboring spel and the fuzzy affinity.    i.e. the fuzzy connectivity of each spel holds the fuzzy path    strength from the seed value.-   Step 6 & 7: If the calculated value in step 4 is larger than the    threshold value, set the connectivity of the current spel to this    value.-   Step 8: Consider all the neighboring spels that have fuzzy affinity    more than 0

The algorithm stops when the queue is empty.

Fuzzy Map

When the fuzzy threshold is set to zero, the algorithm finds the fuzzyconnectivity value for each voxel in the image relative to the seedpoint S₀. This image can be considered as an enhanced image whose voxelsrepresent how strongly they are attached to the seed point. The fuzzymap for the sample scan image is shown in FIG. 8.

The fuzzy map can be used to find the approximate extent of the nodule,by setting a fuzzy threshold to a predetermined value greater than zero.Experimental results using this technique are described below.

Experimental Results—Predetermined Threshold, Mean and StandardDeviation

FIGS. 11 and 12 each show a set of original scan slices, and theapproximate boundary of the nodule superimposed on the original image.In FIG. 11, the threshold was set at 0.92, with predetermined foregroundmean of −100 and standard deviation of 700, while in FIG. 12, thethreshold was set at 0.64, with predetermined foreground mean of 10 andstandard deviation of 1500.

Estimated Region Statistics

The algorithm can find the initial estimate by calculating the standarddeviation and mean of intensity and gradient within a sub-window aroundthe seed point. FIGS. 13 and 14 show the results when the regionstatistics are estimated by the algorithm from the scan image, using theoriginal images of FIGS. 11 and 12 respectively; note that the resultswere obtained after trying various different values of the fuzzythreshold. For FIG. 13, the fuzzy threshold of 0.92 was set with theestimated mean of −255 and standard deviation of 780; while for FIG. 14,the fuzzy threshold of 0.9 was used with an estimated mean of 22 andstandard deviation of 3270.

Reproducibility

The estimated number of voxels included in the nodule region provides atest for reproducibility. The region growing was carried out fromdifferent seed locations and all returned the same region size. This isshown in FIGS. 15 a to 15 c:

9 a) seed:114,170,9

9 b) seed:114, 172, 8

9 c) seed:112, 170, 10

which all produced the same region size of 180 voxels, as shown in FIG.15 d.

Fuzzy Connectivity Image

To illustrate the effect of the fuzzy map, the fuzzy threshold was setto zero and region growing was performed to calculate the fuzzyconnectivity of each voxel within a predetermined radius, withoutrestriction to the mask M₀. The results can be seen in FIGS. 16 a to 16d, where 16 b is a fuzzy map of the nodule shown in 16 a, while 16 d isa fuzzy map of the nodule shown in 16 c.

Comments

The accuracy of the nodule boundary detected using fuzzy thresholdingdepends on selection of a suitable threshold value. Experimental resultsshow that there is no one threshold value suitable for all scans ofisolated and pulmonary lung nodules. Thresholding on the fuzzy map maybe acceptable in some circumstances, but a preferred technique isdescribed below.

5. Contrast Based Region Growing On Fuzzy Map

Instead of setting an arbitrary threshold, the unthresholded fuzzy mapcan be used as an input to further steps to improve the segmentation. Ina preferred embodiment a parameter-free algorithm, using contrast basedregion growing, is applied to the fuzzy map. In this case, the user onlyneeds to provide the seed point, with no threshold adjustment.

The algorithm is applied only to the area within the mask, excluding itsborders and the thorax region. The thorax region is estimated byemploying a coarse segmentation scheme. The algorithm is applied to thefuzzy map of the scan image, rather than the original scan image.

To explain the contrast-based region growing process the following termsare introduced. FIG. 17 shows the intensity profile of an object (abright blob).

The current boundary is the set of pixels adjacent to the current regionduring the growing process. The internal boundary is defined as theboundary produced by the set of connected outermost pixels of thecurrent region. The current region and the two boundaries dynamicallychange during the growing process.

The peripheral contrast of the region is defined as the differencebetween the average grey level of the internal boundary and average greylevel of the current boundary.C _(per) = f _(IB) − f _(CB)where

C_(per) is the peripheral contrast of a region,

f _(IB) is the average fuzzy connectivity of the internal boundary and

f _(CB) is the average fuzzy connectivity of the current boundary.

Another option for calculating peripheral contrast is

$C_{per} = \frac{\sum{\ln{{{Fx}^{2} + {Fy}^{2}}}}}{n}$where

Fx is the x-gradient of the fuzzy connectivity of the internal boundarypoints and

Fy is the y-gradient of the fuzzy connectivity of the internal boundarypoints.

Average Contrast

${Cav} = \frac{\sum{{f_{i} - {\overset{\_}{f}}_{F}}}}{n}$where f_(i) is the fuzzy connectivity for point i on the currentboundary, f _(F) is the mean fuzzy connectivity of the foreground regionF, and n is the number of points on the current boundary

At each iteration of the contrast-based region growing (step 28), onepixel is selected from the current boundary and added to the currentregion. The selection priority of pixels in the current boundary isdetermined on the basis of their intensity and the distance to thecentre of the current region. The combination of intensity and distanceproduces a single priority factor W.

$\begin{matrix}{W = {W_{I}*W_{D}}} & (1) \\{W_{I} = \frac{1}{1 + {{K1}*\left( {f_{i} - {\overset{\_}{f}}_{F}} \right)}}} & (2) \\{W_{D} = \frac{1}{1 + {{K2}*D}}} & (3)\end{matrix}$where

K1 and K2 are the weighting factors. In general, K1+K2≠1. In oneexample, K1=0.01 and K2=0.1.

D is the distance between the candidate pixel and the seed S₀.

When a pixel is added into the current boundary, the internal boundaryand the current boundary are updated. The peripheral contrast is thencalculated and added to a vector which relates to the current regionsize. A schematic smoothed graph of peripheral contrast against regionsize is shown in FIG. 18.

This process continues until the region reaches the pre-defined maximumsize or extent—for example, until the region fills the extended mask M₀.The highest peripheral contrast value obtained during region growing isselected (step 30) as indicating the optimum region, with a boundarymost likely to correspond to that of the nodule. This optimum boundaryis then output (step 32) as the detected boundary of the nodule.

In an alternative embodiment, the region growing is started from a pointdifferent from the optimum seed point S₀, for example, from the pointhaving the highest intensity in the original scan image within theforeground region F. It is then necessary to check that the detectednodule boundary contains the optimum seed point S₀. Hence, regiongrowing from the optimum seed point S₀ is preferred.

In an alternative embodiment, the first maximum peripheral contrastvalue obtained during region growing is selected as indicating theoptimum region, rather than the global maximum value.

Contrast Based Region Growing Algorithm

The algorithm for contrast based region growing is as follows:

-   -   (1) Define the maximum region size.    -   (2) Select the seed point S₀ and add it to the current region.    -   (3) Use second order connectivity (8 neighbors for 2D and 26 for        3D) to find neighbors and first order connectivity (4 for 2D, 6        for 3D) to find/update the current boundary. Sort the points in        the current boundary in ascending order by the priority factor        given by Equation (1) above.    -   (4) Find/update the internal boundary.    -   (5) Calculate the average/peripheral contrast and put the value        in the average/peripheral contrast vector.    -   (6) Find the point with the highest priority W (from Equation 1)        in the current boundary and add to the current region. If the        region reaches the pre-defined maximum size, go to step 7,        otherwise go to step 3.    -   (7) In the average/peripheral contrast vector, find the highest        maximum value (local maximum) and the corresponding region size        and output the current region according to this size. The        boundary of the current region is taken as the extent of the        nodule.

Output

The detected nodule boundary may be output by displaying it as anoutline superimposed on the original scan image. Additionally oralternatively, various nodule metrics may be calculated from the optimumregion and/or its boundary. For example, the presence of spikes on thenodule surface may indicate a malignant nodule. Therefore, a shapemetric calculated from the optimum boundary may be output. Alternativesignificant metrics include the volume or surface area of the optimumregion. The optimum region may be combined with data from the scan imageto determine the mass and/or density of the nodule, which may also beoutput.

Experimental Results

The results of experiments conducted using the algorithm are describedbelow:

Tests with Synthetic Images

FIG. 19 is a synthetic image with a binary circle (pixel size 1291) andthree blurred circles (Gaussian blur with sigma 1, 2 and 3 respectively)derived from the binary one. When the region growing algorithm wasapplied to the three blurred circles (maximum size 2000, K1=0.1,K2=0.01) they all produced a circle as the result.

Using average contrast based region growing, the sizes of the circlesare 1455, 1611 and 1752 pixels respectively. These are much bigger thanthe true value (1291 pixels).

For peripheral contrast based region growing, according to the algorithmabove, the sizes of the circles are 1290, 1272 and 1224 pixelsrespectively. These are very close to the true value (1291 pixels).

Therefore peripheral contrast based region growing appears more suitablefor circular nodule detection. The tests described below all usedperipheral contrast based region growing.

Another test was conducted on a synthetic image with an arrow shapedobject as shown in FIG. 20 and the results are shown in FIG. 21. Theboundary of the arrow-shaped object was correctly identified, showingthat the peripheral contrast based region growing algorithm is alsosuitable for detecting non-circular objects.

Test with Real Image

In this test a CT lung image with an isolated nodule is used, and theperipheral contrast region-growing algorithm was used directly on thescan image, without calculating the fuzzy map. The maximum size is setto 100 pixels, k1=0.01 and k2=0.01 and a seed is put in the middle ofthe bright blob in FIG. 22 a. The result image in FIG. 22 b shows theoptimal region of 2D region growing. The region size is 40 pixels. Theresult of 3D region growing is shown in FIG. 22 c.

Test with Fuzzy Map as Input

FIGS. 23 a to 23 c show the results of a test on a real image as shownin FIG. 23 a, with the fuzzy maps shown in FIG. 23 b and theregion-growing results shown in FIG. 23 c.

Comparative Tests

FIGS. 24 a to 24 c show comparative results using different techniqueson a nodule attached to a blood vessel. FIG. 24 a shows the result usingperipheral contrast based region growing on a real image, FIG. 24 bshows the result using fuzzy connectivity thresholding (threshold of0.6) and FIG. 24 c shows the result of using peripheral contrast basedregion growing on an unthresholded fuzzy map with no predeterminedparameters.

FIGS. 25 a to 25 c show comparative results on a low-contrast noduleusing the same three techniques; for FIG. 25 b, the threshold is 0.805.

FIGS. 26 a to 26 c show comparative results on an isolated nodule usingthe same three techniques; for FIG. 26 b, the threshold is 0.91.

FIGS. 27 a to 27 c show comparative results on a near wall nodule usingthe same three techniques; for FIG. 27 b, the threshold is 0.935.

Conclusion

The preferred embodiment uses a new region growing method. This methoduses a combination of distance and intensity information as the growingmechanism and peripheral contrast as the stop criterion. Aftercomprehensive tests with synthetic images and real images it was foundthat this region growing method can provide very good results forisolated or pulmonary nodules in CT lung images, especially when it iscombined with a fuzzy map. It can be used to detect isolated orpulmonary lung nodules semi-automatically.

Alternative Embodiments

The embodiments above are described by way of example, and are notintended to limit the scope of the invention. Various alternatives maybe envisaged which nevertheless fall within the scope of the claims. Aswill be apparent from the above discussion, the method can be performedon a 2D image consisting of a single CT slice, or a 3D image consistingof consecutive CT slices.

1. A computed tomography (CT) method comprising: receiving CT scan imagedata representative of a portion of a body and an indication of a seedpoint within a nodule in a CT scan image of the portion of the body;performing by computation using a computing device fine segmentationbased on local contrast of the CT scan image, to separate foregroundareas from background areas of the CT scan image; defining bycomputation from the CT scan image a mask including an object containingthe seed point, connected foreground area, and background areasurrounding the object, and excluding other foreground objects;computing the connectivity of points of the CT scan image to the seedpoint; and applying by computation a selective criterion to theconnectivity of the points of the CT scan image to determine the extentof the nodule in the CT scan image, wherein the mask limits thedetermined extent of the nodule in the CT scan image.
 2. The method ofclaim 1, wherein the connectivity is determined only on the basis ofpoints within the mask.
 3. The method of claim 1, wherein the finesegmentation applies a threshold based on the local contrast to identifya point as belonging to a foreground area.
 4. The method of claim 3,wherein the local contrast is determined only within a local masksurrounding the point.
 5. The method of claim 4, wherein the thresholdis set as a mean of centroids of local intensity values above and belowthe threshold, offset by a predetermined value.
 6. The method of claim4, wherein the CT scan image is three-dimensional and the local mask isthree-dimensional.
 7. The method of claim 1, wherein the finesegmentation includes redefining an area of background enclosed by aforeground area as foreground.
 8. The method of claim 7, includingfitting a shape to the foreground area, and setting an interior of theshape as foreground.
 9. The method of claim 1, wherein the connectedforeground area is determined by performing region growing of theforeground area including the seed point.
 10. The method of claim 9,wherein the CT scan image is three-dimensional and the region growing isperformed in three dimensions to obtain the connected foreground area.11. The method of claim 10, wherein the three-dimensional region growingis performed by identifying foreground areas in adjacent slices of theCT scan image connected to a foreground area containing the seed point.12. The method of claim 11, wherein the foreground areas in adjacentslices are detected by displacing the seed point to adjacent slices ofthe CT scan image, and region growing from the displaced seed point ifthe displaced seed point is within a foreground area.
 13. The method ofclaim 12, wherein the displaced seed point has a position within theslice corresponding to the centre of the connected foreground area inthe slice from which the seed point was displaced.
 14. The method ofclaim 9, wherein the mask is defined by expanding the connectedforeground area to include the background area surrounding the connectedforeground area and to exclude other foreground areas not connected tothe connected foreground area.
 15. The method of claim 14, wherein themask is expanded so as to contain a predetermined proportion of thebackground area to the connected foreground area.
 16. The method ofclaim 15, wherein the mask contains approximately equal foreground andbackground areas.
 17. The method of claim 1, wherein the seed point isdetermined by receiving an indication of an initial seed point, anditeratively determining the mask based on a current seed point andselecting a point within a current connected foreground area as a newseed point, until masks determined by successive iterations converge.18. The method of claim 17, wherein a point of high intensity within theconnected foreground area is selected as the new seed point.
 19. Themethod of claim 17, wherein a central point within the connectedforeground area is selected as the new seed point.
 20. The method ofclaim 17, wherein the initial seed point is selected by a user.
 21. Themethod of claim 1, wherein the selective criterion includes performingregion growing on a map of the connectivity.
 22. The method of claim 21,wherein the region growing comprises growing a region within theconnectivity map, finding the maximum boundary contrast during theregion growing, and identifying the region corresponding to the maximumboundary contrast as defining the extent of the nodule.
 23. The methodof claim 21, wherein the region growing is performed by selecting apoint on a boundary of a region based on a priority factor.
 24. Themethod of claim 23, wherein the priority factor is based on theconnectivity of the point, such that points of higher connectivity havea higher priority factor.
 25. The method of claim 23, wherein thepriority factor is based on the distance of the point from the centre ofthe region, such that points closer to the centre of the region have ahigher priority factor.
 26. The method of claim 1, wherein theconnectivity is based on an affinity between adjacent points.
 27. Themethod of claim 26, wherein the connectivity is based on the affinitiesof points along a path between a point and the seed point.
 28. Themethod of claim 27, wherein the connectivity is based on the weakestaffinity between adjacent points along the path.
 29. The method of claim28, wherein the connectivity is based on the path of strongest affinitybetween a point and the seed point.
 30. The method of claim 26, whereinthe affinity is a function of statistical variation of intensity aroundthe seed point.
 31. The method of claim 30, wherein the statisticalvariation includes the mean and standard deviation of intensity andgradient.
 32. The method of claim 30, wherein the affinity is a functionof statistical variation of intensity within the mask.
 33. The method ofclaim 32, wherein the standard deviation is adjusted as a function ofstatistical variation in the background area within the mask, such thatthe background area has minimal but finite connectivity with the seedpoint.
 34. The method of claim 1, wherein the selective criterioncomprises a connectivity threshold.
 35. The method of claim 1, includingoutputting an indication of the extent of the nodule.
 36. A computedtomography (CT) method, comprising: (a) receiving CT scan image datarepresentative of a portion of a body and an indication of a seed pointwithin a nodule in a CT scan image of the portion of the body; (b)performing by computation using a computing device fine segmentation toseparate the CT scan image around the seed point into foreground andbackground, using a threshold based on local contrast of the CT scanimage; (c) setting background points enclosed by foreground points asforeground points; (d) growing by computation a foreground regioncontaining the seed Point; (e) expanding by computation the foregroundregion to include background points while excluding foreground pointsnot included within the foreground region, to create a mask; (f) settinga point within the centre of the foreground region and having a highintensity as a new seed point; (g) repeating steps (b) to (f) with thenew seed point until the masks from successive iterations converge; (h)deriving by computation a fuzzy connectivity map defining theconnectivity of points within the mask to the seed point; and (i)determining the extent of the nodule from the fuzzy connectivity map.37. The method of claim 36, wherein (i) comprises growing by computationa connectivity region from the seed point within the fuzzy connectivitymap, and outputting the region having the highest boundary contrast asthe extent of the nodule.
 38. A computer-readable medium havinginstructions stored thereon that, if executed by a computing device,cause the computing device to perform a computed tomography (CT) method,the method comprising: receiving CT scan image data representative ofportion of a body and an indication of a seed point within a nodule of aCT scan image of the portion of the body; performing fine segmentationbased on local contrast of CT scan image, to separate foreground areasfrom background areas of the CT scan image; defining from the CT scanimage a mask including an object containing the seed point, connectedforeground area, and background area surrounding the object, andexcluding other foreground objects; computing the connectivity of pointsof the CT scan image to the seed point; and applying a selectivecriterion to the connectivity of the points to identify an extent of thenodule, wherein the mask limits the extent of the nodule in the CT scanimage.
 39. A computer-readable medium having instructions stored thereonthat, if executed by a computing device, cause the computing device toperform a computed tomography(CT) method, the method comprising: (a)receiving CT scan image data representative of a portion of a body andan indication of a seed point within a nodule of a CT scan image of theportion of the body; (b) performing fine segmentation to separate the CTscan image around the seed point into foreground and background, using athreshold based on the local contrast; (c) setting background pointsenclosed by foreground points as foreground points; (d) growing aforeground region containing the seed point; (e) expanding theforeground region to include background points while excludingforeground points not included within the foreground region, to create amask; (f) setting a point within the foreground region and having a highintensity as a new seed point; (g) repeating steps (b) to (f) with thenew seed point until the masks from successive iterations converge; (h)deriving a fuzzy connectivity map defining the connectivity of pointswithin the mask to the seed point; and (i) determining an extent of thenodule from the fuzzy connectivity map.
 40. A computed tomography (CT)method comprising: receiving CT scan image data representative of aportion of a body and an indication of a seed point within a nodule in aCT scan image of the portion of the body; performing by computationusing a computing device fine segmentation to separate foreground areasfrom background areas of the CT scan image; defining by computation amask including an object containing the seed point, connected foregroundarea, and background area surrounding the object, and excluding otherforeground objects, wherein the foreground area is determined byperforming region growing of the foreground area including the seedpoint, wherein the CT scan image is three-dimensional and the regiongrowing is performed in three dimensions to obtain the connectedforeground area, and wherein the region growing is performed byidentifying foreground areas in adjacent slices of the scan imageconnected to a foreground area containing the seed point; computing theconnectivity of points of the image to the seed point; and applying bycomputing a selective criterion to the connectivity of the points toidentify the extent of the nodule.
 41. The method of claim 40, whereinthe foreground areas in adjacent slices are detected by displacing theseed point to adjacent slices of the CT scan image, and region growingfrom the displaced seed point if the displaced seed point is within aforeground area.
 42. The method of claim 41, wherein the displaced seedpoint has a position within the slice corresponding to the centre of theconnected foreground area in the slice from which the seed point wasdisplaced.
 43. A computed tomography (CT) method comprising: receivingCT scan image data representative of a portion of a body and anindication of a seed point within a nodule in a CT scan image of theportion of the body; performing by computation using a computing devicefine segmentation to separate foreground areas from background areas ofthe CT scan image; defining by computation a mask including an objectcontaining the seed point, connected foreground area, and the backgroundarea surrounding the object, and excluding other foreground objects,wherein the connected foreground area is determined by performing regiongrowing of the foreground area including the seed point, wherein themask is defined by expanding the connected foreground area to includethe background area surrounding the connected foreground area and toexclude other foreground area not connected to the connected foregroundarea, and wherein the mask is expanded so as to contain a predeterminedproportion of the background area to the connected foreground; computingthe connectivity of points of CT scan the image to the seed point; andapplying by computation a selective criterion to the connectivity of thepoints to identify the extent of the nodule.
 44. The method of claim 43,wherein the mask contains approximately equal foreground and backgroundareas.
 45. A computed tomography (CT) method comprising: receiving CTscan image data representative of a portion of a body and an indicationof a seed point within a nodule in a CT scan image of the portion of thebody; defining by computation using a computing device a mask includingan object containing the seed point, connected foreground area, andbackground area surrounding the object, and excluding other foregroundobjects, wherein the seed point is determined by receiving an indicationof an initial seed point, and iteratively determining the mask based ona current seed point and selecting a point of high intensity within acurrent connected foreground area as a new seed point, until masksdetermined by successive iterations converge; computing the connectivityof points of the CT scan image to the seed point; and applying bycomputation a selective criterion to the connectivity of the points toidentify the extent of the nodule.
 46. The method of claim 45, wherein apoint of high intensity within the connected foreground area is selectedas the new seed point.
 47. The method of claim 45, wherein a centralpoint within the connected foreground area is selected as the new seedpoint.
 48. The method of claim 45, wherein the initial seed point isselected by a user.
 49. A computed tomography (CT) method comprising:receiving CT scan image data representative of a portion of a body andan indication of a seed point within a nodule in a CT scan image of theportion of the body; defining by computation using a computing device amask including an object containing the seed point and background areasurrounding the object, and excluding other foreground objects;computing the connectivity of points of the CT scan image to the seedpoint; and applying by computation a selective criterion to theconnectivity of the points to identify the extent of the nodule, whereinthe selective criterion includes performing region growing on a map ofthe connectivity, and wherein the region growing comprises growing aregion within the connectivity map, finding the maximum boundarycontrast during the region growing, and identifying the regioncorresponding to the maximum boundary contrast as defining the extent ofthe nodule.
 50. A computed tomography (CT) method comprising: receivingCT scan image data representative of a portion of a body and anindication of a seed point within a nodule in a CT scan image of theportion of the body; defining by computation using a computing device amask including an object containing the seed point and background areasurrounding the object, and excluding other foreground objects;computing the connectivity of points of the CT scan image to the seedpoint; and applying by computation a selective criterion to theconnectivity of the points to identify the extent of the nodule, whereinthe selective criterion includes performing region growing on a map ofthe connectivity, and wherein the region growing is performed byselecting a point on a boundary of a region based on a priority factor.51. The method of claim 50, wherein the priority factor is based on theconnectivity of the point, such that points of higher connectivity havea higher priority factor.
 52. The method of claim 50, wherein thepriority factor is based on the distance of the point from the centre ofthe region, such that points closer to the centre of the region have ahigher priority factor.
 53. A computed tomography (CT) methodcomprising: receiving CT scan image data representative of a portion ofa body and an indication of a seed point within a nodule in a CT scanimage of the portion of the body; computing using a computing device theconnectivity of points of the image to the seed point, wherein theconnectivity is based on an affinity between adjacent points, theaffinities of points along a path between a point and the seed point,the weakest affinity between adjacent points along the path, and thepath of strongest affinity between a point and the seed point; andapplying by computation a selective criterion to the connectivity of thepoints to identify the extent of the nodule.
 54. A computed tomography(CT) method comprising: receiving CT scan image data representative of aportion of a body and an indication of a seed point within a nodule in aCT scan image of the portion of the body; computing using a computingdevice the connectivity of points of the CT scan image to the seedpoint, wherein the connectivity is based on an affinity between adjacentpoints, wherein the affinity is a function of statistical variation ofintensity around the seed point, and wherein the statistical variationincludes the mean and standard deviation of intensity and gradient; andapplying by computation a selective criterion to the connectivity of thepoints to identify the extent of the nodule.
 55. A computed tomography(CT) method comprising: receiving CT scan image data representative of aportion of a body and an indication of a seed point within a nodule in aCT scan image of the portion of the body; computing using a computingdevice the connectivity the connectivity of points of the image to theseed point, wherein the connectivity is based on an affinity betweenadjacent points, wherein the affinity is a function of statisticalvariation of intensity around the seed point, and wherein the affinityis a function of statistical variation of intensity within the mask; andapplying by computation a selective criterion to the connectivity of thepoints to identify the extent of the nodule.
 56. The method of claim 55,wherein the standard deviation is adjusted as a function of statisticalvariation in the background area within the mask, such that thebackground area has minimal but finite connectivity with the seed point.